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Global Asymptotic Stability in a Rational Difference Equation

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Author(s): İbrahim Yalçınkaya

Journal: Selçuk Journal of Applied Mathematics
ISSN 1302-7980

Volume: 6;
Issue: 2;
Start page: 59;
Date: 2005;
Original page

Keywords: Rational difference equation | Locally asymptotic stable | Global asymptotic stability | Semicycle | Equilibrium point.

ABSTRACT
In this paper a sufficient condition is obtained for the global asmptotic stability of the following rational difference equation;x_{n+1}=((x_{n}+x_{n-1})/(x_{n}x_{n-1}+1)), n=0,1,2,...where aε[0,∞) and the initial values x₋₂,x₋₁,x₀ε(0,∞).